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Proposition: Sum of Binomial Coefficients II

For any element of a ring \(x\in(R,+,\cdot) \) and any natural number \(n\ge 1\) the following sum formula holds:

\[\sum_{k=0}^nk\binom nk(1-x)^{n-k}x^k=nx.\]

Table of Contents

Proofs: 1

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Proofs: 1

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References

Bibliography

1. Bosch, Karl: "Elementare Einführung in die Wahrscheinlichkeitsrechnung", vieweg Studium, 1995, 6th Edition